\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t57\_circtrm1 (TMR5NdnPhDJpVsStRh7YP8YpiFTtchFp6KE)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_msafree2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_msafree2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r5\_circtrm1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r3\_circtrm1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r4\_circtrm1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ k2\_funct\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_msafree2~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh \\
v11\_struct\_0~X1){\unicdcdcdhd}((v2\_msafree2~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~\\
X3){\unicdcdcdhd}(v1\_funct\_1~X3)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v4\_msualg\_1~X4~X0){\unicdcdcdhd}((v4\_msafree2~\\
X4~X0){\unicdcdcdhd}(l3\_msualg\_1~X4~X0))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v4\_msualg\_1~X5~X1){\unicdcdcdhd}\\
((v4\_msafree2~X5~X1){\unicdcdcdhd}(l3\_msualg\_1~X5~X1))){\unicdbdjdcd}((r5\_circtrm1~X0~X1~\\
X2~X3~X4~X5){\unicdbdjdcd}(r3\_circtrm1~X0~X1~X2)))))))\end{array}
\label{hyp:ehfdddpfdgjgchdgehchngbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_msafree2~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh \\
v11\_struct\_0~X1){\unicdcdcdhd}((v2\_msafree2~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~\\
X3){\unicdcdcdhd}(v1\_funct\_1~X3)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v4\_msualg\_1~X4~X0){\unicdcdcdhd}((v4\_msafree2~\\
X4~X0){\unicdcdcdhd}(l3\_msualg\_1~X4~X0))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v4\_msualg\_1~X5~X1){\unicdcdcdhd}\\
((v4\_msafree2~X5~X1){\unicdcdcdhd}(l3\_msualg\_1~X5~X1))){\unicdbdjdcd}(((r4\_circtrm1~X0~\\
X1~X2~X3~X4~X5){\unicdcdcdhd}(r3\_circtrm1~X0~X1~X2)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~\\
X6~(k4\_card\_3~(u3\_msualg\_1~X1~X5))){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~\\
X7~(k4\_card\_3~(u3\_msualg\_1~X0~X4))){\unicdbdjdcd}((X7=k3\_relat\_1~X2~X6){\unicdbdjdcd}({\unicdcdadad} X8 .  \\
(m1\_subset\_1~X8~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_facirc\_1~X0~X4~X7~X8){\unicdbdjded}(\\
r1\_facirc\_1~X1~X5~X6~(k1\_funct\_1~X2~X8)))))))))))))\end{array}
\label{hyp:ehedjdpfdgjgchdgehchngbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}(v1\_funct\_1~\\
X3)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v4\_msualg\_1~X4~X0){\unicdcdcdhd}(l3\_msualg\_1~X4~X0)){\unicdbdjdcd}(\\
{\unicdcdadad} X5 .  ((v4\_msualg\_1~X5~X1){\unicdcdcdhd}(l3\_msualg\_1~X5~X1)){\unicdbdjdcd}((r5\_circtrm1~\\
X0~X1~X2~X3~X4~X5){\unicdbdjded}((r4\_circtrm1~X0~X1~X2~X3~X4~X5){\unicdcdcdhd}(r4\_circtrm1~X1~\\
X0~(k2\_funct\_1~X2)~(k2\_funct\_1~X3)~X5~X4))))))))\end{array}
\label{hyp:egbdddpfdgjgchdgehchngbd}
\end{equation}
\begin{theorem}\label{thm:ehfdhdpfdgjgchdgehchngbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_msafree2~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh \\
v11\_struct\_0~X1){\unicdcdcdhd}((v2\_msafree2~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~\\
X3){\unicdcdcdhd}(v1\_funct\_1~X3)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v4\_msualg\_1~X4~X1){\unicdcdcdhd}((v4\_msafree2~\\
X4~X1){\unicdcdcdhd}(l3\_msualg\_1~X4~X1))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v4\_msualg\_1~X5~X0){\unicdcdcdhd}\\
((v4\_msafree2~X5~X0){\unicdcdcdhd}(l3\_msualg\_1~X5~X0))){\unicdbdjdcd}((r5\_circtrm1~X1~X0~\\
X2~X3~X4~X5){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(k4\_card\_3~(u3\_msualg\_1~\\
X1~X4))){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(k4\_card\_3~(u3\_msualg\_1~\\
X0~X5))){\unicdbdjdcd}((X6=k3\_relat\_1~X2~X7){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(\\
u1\_struct\_0~X1)){\unicdbdjdcd}((r1\_facirc\_1~X1~X4~X6~X8){\unicdbdjded}(r1\_facirc\_1~X0~X5~\\
X7~(k1\_funct\_1~X2~X8)))))))))))))\end{array}$$
\end{theorem}
\end{document}
